Development of a musculoskeletal model of the wrist to predict frictional work dissipated due to tendon gliding resistance in the carpal tunnel.

Carpal tunnel syndrome is an entrapment neuropathy that has been associated with the aggravation of tendon gliding resistance due to forceful, high velocity, awkwardly angled, and repetitive wrist motions. Cadaveric and epidemiological studies have shown that combinations of these risk factors have a more than additive effect. The aim of the current study was to develop a musculoskeletal model of the wrist that could evaluate these risk factors by simulating frictional work dissipated due to the gliding resistance of the third flexor digitorum superficialis tendon. Three flexion angle zones, three extension angle zones, five levels of task repetitiveness, and five levels of task effort were derived from ergonomic standards. Of the simulations performed by systematically combining these parameters, the extreme wrist flexion zone, at peak task repetitiveness and effort, dissipated the most frictional work. This zone dissipated approximately double the amount of frictional work compared to its equivalent zone in extension. For all motions, a multiplicative effect of the combination of task repetitiveness and effort on frictional work was identified by the musculoskeletal model, corroborating previous epidemiological and experimental studies. Overall, these results suggest that the ergonomic standards for wrist flexion-extension may need to be adjusted to reflect equivalent biomechanical impact and that workplace tasks should be designed to minimise exposure to combinations of highly repetitive and highly forceful work, especially when the wrist is highly flexed.

Tailoring anatomical muscle paths: a sheath-like solution for muscle routing in musculoskeletal computer models.

Muscle wrapping geometry has a major impact on the muscle force as well as the torque onto the joint exerted by this muscle since these torques highly depend on the muscle's line of action or, in other words, the muscle moment arm. Most common redirection methods focus on two-dimensional motions and optimise path geometry for only one isolated movement, either flexion, abduction or rotation, instead of covering all degrees of freedom (DOFs). Others can only imitate anatomical paths in a small working range or for single joint movements. For biomechanical simulations of sweeping movements like running or throwing, however, a correct representation of muscle paths for a large range of joint configurations is mandatory. We introduce a new computational algorithm for modelling the muscle path in three-dimensional biomechanical simulations, based on a model description of muscles as massless, visco-elastic strands and the assumption that the muscle acts along a continuous path consisting of piecewise straight lines. In the presented approach, anatomical constraints including bones, tendon sheaths and other surrounding tissue are represented by areas the muscle has to pass. We model these redirection constraints as ellipses, allowing the muscle path to move within these areas and along their frictionless, inner edges. We show that - by only adjusting ellipse parameters - we are able to achieve reasonable moment arms for all (DOFs) and for a large range of joint configurations of uniarticular muscles as well as muscles spanning more than one joint - even for complex geometries.

The influence of biophysical muscle properties on simulating fast human arm movements.

Computational modeling provides a framework to understand human movement control. For this approach, physiologically motivated and experimentally validated models are required to predict the dynamic interplay of the neuronal controller with the musculoskeletal biophysics. Previous studies show, that an adequate model of arm movements should consider muscle fiber contraction dynamics, parallel and serial elasticities, and activation dynamics. Numerous validated macroscopic model representations of these structures and processes exist. In this study, the influence of these structures and processes on maximum movement velocity of goal-directed arm movements was investigated by varying their mathematical model descriptions. It was found that the movement velocity strongly depends on the pre-activation of the muscles (differences up to 91.6%) and the model representing activation dynamics (differences up to 43.3%). Looking at the influence of the active muscle fibers (contractile element), the simulations reveal that velocities systematically differ depending on the width of the force-length relation (differences up to 17.4%). The series elasticity of the tendon influences the arm velocity up to 7.6%. In conclusion, in fast goal-directed arm movements from an equilibrium position, the modeling of the biophysical muscle properties influences the simulation results. To reliably distinguish between mathematical formulations by experimental validation, the initial muscular activity and the activation dynamics have to be modeled validly, as their influence excels. To this end, further experiments systematically varying the initial muscular activity would be needed.

Quantifying control effort of biological and technical movements: an information-entropy-based approach.

In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I=32 bits versus I=660 bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.

Hill-type muscle model with serial damping and eccentric force-velocity relation.

Hill-type muscle models are commonly used in biomechanical simulations to predict passive and active muscle forces. Here, a model is presented which consists of four elements: a contractile element with force-length and force-velocity relations for concentric and eccentric contractions, a parallel elastic element, a series elastic element, and a serial damping element. With this, it combines previously published effects relevant for muscular contraction, i.e. serial damping and eccentric force-velocity relation. The model is exemplarily applied to arm movements. The more realistic representation of the eccentric force-velocity relation results in human-like elbow-joint flexion. The model is provided as ready to use Matlab and Simulink code.

Nature as an engineer: one simple concept of a bio-inspired functional artificial muscle.

The biological muscle is a powerful, flexible and versatile actuator. Its intrinsic characteristics determine the way how movements are generated and controlled. Robotic and prosthetic applications expect to profit from relying on bio-inspired actuators which exhibit natural (muscle-like) characteristics. As of today, when constructing a technical actuator, it is not possible to copy the exact molecular structure of a biological muscle. Alternatively, the question may be put how its characteristics can be realized with known mechanical components. Recently, a mechanical construct for an artificial muscle was proposed, which exhibits hyperbolic force-velocity characteristics. In this paper, we promote the constructing concept which is made by substantiating the mechanical design of biological muscle by a simple model, proving the feasibility of its real-world implementation, and checking their output both for mutual consistency and agreement with biological measurements. In particular, the relations of force, enthalpy rate and mechanical efficiency versus contraction velocity of both the construct's technical implementation and its numerical model were determined in quick-release experiments. All model predictions for these relations and the hardware results are now in good agreement with the biological literature. We conclude that the construct represents a mechanical concept of natural actuation, which is suitable for laying down some useful suggestions when designing bio-inspired actuators.

Integration of intrinsic muscle properties, feed-forward and feedback signals for generating and stabilizing hopping.

It was hypothesized that a tight integration of feed-forward and feedback-driven muscle activation with the characteristic intrinsic muscle properties is a key feature of locomotion in challenging environments. In this simulation study it was investigated whether a combination of feed-forward and feedback signals improves hopping stability compared with those simulations with one individual type of activation. In a reduced one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements), the level of detail of the muscle's force-length-velocity relation and the type of activation generation (feed-forward, feedback and combination of both) were varied to test their influence on periodic hopping. The stability of the hopping patterns was evaluated by return map analysis. It was found that the combination of feed-forward and proprioceptive feedback improved hopping stability. Furthermore, the nonlinear Hill-type representation of intrinsic muscle properties led to a faster reduction of perturbations than a linear approximation, independent of the type of activation. The results emphasize the ability of organisms to exploit the stabilizing properties of intrinsic muscle characteristics.

Proof of concept of an artificial muscle: theoretical model, numerical model, and hardware experiment.

Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) exhibits operating points with hyperbolic force-velocity dependency. In this paper, the contraction dynamics of this CE concept were analyzed in a numerical simulation of quick release experiments against different loads. A hyperbolic force-velocity relation was found. The results correspond to measurements of the contraction dynamics of a technical prototype. Deviations from the theoretical prediction could partly be explained by the low stiffness of the SE, which was modeled analog to the metal spring in the hardware prototype. The numerical model and hardware prototype together, are a proof of this CE concept and can be seen as a well-founded starting point for the development of Hill-type artificial muscles. This opens up new vistas for the technical realization of natural movements with rehabilitation devices.

The role of intrinsic muscle properties for stable hopping--stability is achieved by the force-velocity relation.

A reductionist approach was presented to investigate which level of detail of the physiological muscle is required for stable locomotion. Periodic movements of a simplified one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements) were analyzed. Force-length and force-velocity relations of the muscle were varied in three levels of approximation (constant, linear and Hill-shaped nonlinear) resulting in nine different hopping models of different complexity. Stability of these models was evaluated by return map analysis and the performance by the maximum hopping height. The simplest model (constant force-length and constant force-velocity relations) outperformed all others in the maximum hopping height but was unstable. Stable hopping was achieved with linear and Hill-shaped nonlinear characteristic of the force-velocity relation. The characteristics of the force-length relation marginally influenced hopping stability. The results of this approach indicate that the intrinsic properties of the contractile element are responsible for stabilization of periodic movements. This connotes that (a) complex movements like legged locomotion could benefit from stabilizing effects of muscle properties, and (b) technical systems could benefit from the emerging stability when implementing biological characteristics into artificial muscles.